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एक टाइल व्यवस्था \(x^2+15x+54\) को आयत बनाती है। किन स्थिर पट्टियों से यह व्यवस्था संभव है?
A tile arrangement \(x^2+15x+54\) forms a rectangle. Which constant strips make this arrangement possible?
#area-tiles
#factorisation
#visual
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A (2) और (27) / (2) and (27)
B (5) और (10) / (5) and (10)
C (3) और (18) / (3) and (18)
D (6) और (9) / (6) and (9)
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Correct Answer
D. (6) और (9) / (6) and (9)
Step 1
Concept
(6+9=15) and \(6\times9=54\). In exams, match both sum and product.
Step 2
Why this answer is correct
The correct answer is D. (6) और (9) / (6) and (9). (6+9=15) and \(6\times9=54\). In exams, match both sum and product.
Step 3
Exam Tip
(6+9=15) और \(6\times9=54\) है। परीक्षा में योग और गुणनफल दोनों मिलाएँ।
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एक मॉडल \(x^2+5x-36\) को आयत में बदलता है। कौन-सी भुजाएँ सही हैं?
A model changes \(x^2+5x-36\) into a rectangle. Which sides are correct?
#factorisation
#signed-tiles
#visual
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A (x+12) और (x-3) / (x+12) and (x-3)
B (x+6) और (x-6) / (x+6) and (x-6)
C (x+9) और (x-4) / (x+9) and (x-4)
D (x-9) और (x+4) / (x-9) and (x+4)
Explanation opens after your attempt
Correct Answer
C. (x+9) और (x-4) / (x+9) and (x-4)
Step 1
Concept
(9+(-4)=5) and (9\cdot(-4)=-36). In exams, check signs in both sum and product.
Step 2
Why this answer is correct
The correct answer is C. (x+9) और (x-4) / (x+9) and (x-4). (9+(-4)=5) and (9\cdot(-4)=-36). In exams, check signs in both sum and product.
Step 3
Exam Tip
(9+(-4)=5) और (9\cdot(-4)=-36) है। परीक्षा में योग और गुणनफल में चिन्ह जाँचें।
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एक मॉडल \(2x^2+7x+3\) को आयत में बदलता है। कौन-सा विभाजन सही दृश्य निर्माण देता है?
A model converts \(2x^2+7x+3\) into a rectangle. Which split gives the correct visual construction?
#area-factorisation
#split-middle
#visual
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A \(2x^2+2x+5x+3\)
B \(2x^2+x+6x+3\)
C \(2x^2+3x+4x+3\)
D \(2x^2+7x+7+3\)
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Correct Answer
B. \(2x^2+x+6x+3\)
Step 1
Concept
\(1\cdot6=6\) and \(2\cdot3=6\), so grouping (x+6x) gives ((2x+1)(x+3)). In exams, verify the middle split by area grouping.
Step 2
Why this answer is correct
The correct answer is B. \(2x^2+x+6x+3\). \(1\cdot6=6\) and \(2\cdot3=6\), so grouping (x+6x) gives ((2x+1)(x+3)). In exams, verify the middle split by area grouping.
Step 3
Exam Tip
\(1\cdot6=6\) और \(2\cdot3=6\), इसलिए (x+6x) समूह से ((2x+1)(x+3)) बनता है। परीक्षा में मध्य पद विभाजन को क्षेत्रफल समूह से जाँचें।
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यदि \(x^2-12x+35\) की टाइलों से आयत बने, तो कौन-सी भुजाएँ मॉडल को सही बनाती हैं?
If tiles of \(x^2-12x+35\) form a rectangle, which sides make the model correct?
#signed-factorisation
#area-tiles
#visual
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A (x-1) और (x-35) / (x-1) and (x-35)
B (x+5) और (x+7) / (x+5) and (x+7)
C (x-5) और (x-7) / (x-5) and (x-7)
D (x+12) और (x-35) / (x+12) and (x-35)
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Correct Answer
C. (x-5) और (x-7) / (x-5) and (x-7)
Step 1
Concept
(-5+(-7)=-12) and ((-5)(-7)=35). In exams, product of two negative constants is positive.
Step 2
Why this answer is correct
The correct answer is C. (x-5) और (x-7) / (x-5) and (x-7). (-5+(-7)=-12) and ((-5)(-7)=35). In exams, product of two negative constants is positive.
Step 3
Exam Tip
(-5+(-7)=-12) और ((-5)(-7)=35) है। परीक्षा में दो ऋणात्मक स्थिर भागों का गुणन धनात्मक होता है।
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